E. Alòs and M. Fukasawa: The asymptotic expansion of the regular discretization error of Itô integrals. Math. Finance 31 (2021), pp. 323–365. MR4205885
E. Azmoodeh and L. Viitasaari: Rate of convergence for discretization of integrals with respect to fractional Brownian motion. Journal of Theoretical Probability 28 (2015), no. 1, pp. 396–422. MR3320973
W. Beckner: Geometric inequalities in Fourier analysis. In Essays on Fourier Analysis in Honor of Elias M. Stein, Princeton University Press, Princeton, NJ (1995), pp. 36–68. MR1315541
F. Comte and E. Renault. Long memory in continuous-time stochastic volatility models. Math. Finance 8 (1998), no. 4, pp. 291–323. MR1645101
J.M Corcuera, D. Nualart and M. Podolskij: Asymptotics of weighted random sums Communications in Applied and Industrial Mathematics 6, no. 1 (2014). MR3277312
L. Coutin, D. Nualart and C.A. Tudor: Tanaka formula for the fractional Brownian motion. Stochastic processes and their applications 94 (2001), no. 2, pp. 301–315. MR1840834
C. Döbler, M. Kasprzak and G. Peccati: Functional Convergence of U-processes with SizeDependent Kernels Ann. Appl. Probab., to appear. MR4386536
P. K. Friz and M. Hairer: A course on rough paths Universitext. Springer, Cham, 2014. With an introduction to regularity structures. MR3289027
M. Fukasawa: Discretization error of stochastic integrals. Ann. Appl. Probab. 21 (2011), no. 4, pp. 1436–1465. MR2857453
A. Garsia, E. Rodemich, H. Rumsey and M. Rosenblatt: A real variable lemma and the continuity of paths of some Gaussian processes Indiana University Mathematics Journal 20 (1970) no 6, pp. 565–578. MR0267632
E. Gobet and E. Temam: Discrete time hedging errors for options with irregular payoffs. Finance and Stochastics 5 (2001), no. 3, pp. 357–367. MR1849426
M. Gubinelli: Controlling rough paths Journal of Functional Analysis 216 (2004) no 1, pp. 86–140 MR2091358
Y. Hu, Y. Liu and D. Nualart: Rate of convergence and asymptotic error distribution of Euler approximation schemes for fractional diffusions. Ann. Appl. Probab. 26 (2016), no. 2, pp. 1147–1207. MR3476635
J. Jacod and P. Protter: Asymptotic error distributions for the Euler method for stochastic differential equations. Ann. Probab. 26 (1998), no. 1, pp. 267–307. MR1617049
R. Klein and E. Gine: On quadratic variation of processes with Gaussian increments. Ann. Probab (1975) pp. 716–721. MR0378070
A.N. Kolmogorov: The Wiener spiral and some other interesting curves in Hilbert space. Dokl. Akad. Nauk SSSR 26 (1940), no. 2, pp. 115–118. MR0009098
W.E. Leland, M.S. Taqqu, W. Willinger and D.V. Wilson: On the self-similar nature of ethernet traffic (extended version). IEEE/ACM Transactions on networking 2 (1994), no. 1, pp. 1–15.
C. Lindberg and H. Rootzén: Error distributions for random grid approximations of multidimensional stochastic integrals. Ann. Appl. Probab. 23 (2013), no. 2, pp. 834–857. MR3059277
Y. Liu and S. Tindel: Discrete rough paths and limit theorems. Ann. Inst. H. Poincaré Probab. Statist. 56, no. 3 (2020), pp. 1730–1774. MR4116706
B.B. Mandelbrot and J.W. Van Ness: Fractional Brownian motions, fractional noises and applications. SIAM Rev. 10 (1968), pp. 422–437. MR0242239
T. Mikosch, S. Resnick, H. Rootzén and A. Stegeman. Is network traffic approximated by stable Lévy motion or fractional Brownian motion? Ann. Appl. Probab. 12 (2002), no. 1, pp. 23–68. MR1890056
F.J. Molz, H.H. Liu and J. Szulga: Fractional Brownian motion and fractional Gaussian noise in subsurface hydrology: A review, presentation of fundamental properties, and extensions. Water Resources Research 33 (1997), no. 10, pp. 2273–2286.
A. Neuenkirch and I. Nourdin: Exact rate of convergence of some approximation schemes associated to SDEs driven by a fractional Brownian motion. J. Theoret. Probab. 20 (2007), no. 4, pp. 871–899. MR2359060
I. Nourdin, D. Nualart and C.A. Tudor: Central and non-central limit theorems for weighted power variations of fractionnal Brownian motion Ann. Inst. H. Poincaré Probab. Statist. 46 (2010), no 4, pp 1055–1079. MR2744886
I. Nourdin, A. Réveillac and J. Swanson: The weak Stratonovich integral with respect to fractional Brownian motion with Hurst parameter 1/6. Electronic Journal of Probability 15 (2010), pp. 2117–2162. MR2745728
I. Nourdin and G. Peccati: Normal approximation with Malliavin calculus: from Stein’s method to universality Volume 192. Cambridge University Press, 2012. MR2962301
D. Nualart: The Malliavin calculus and related topics Volume 1995. Springer, 2006. MR1344217
G. Peccati and C. A. Tudor: Gaussian limits for vector-valued multiple stochastic integrals. In Séminaire de Probabilités XXXVIII, pp. 247–262, Springer, 2005. MR2126978
B. Pesquet-Popescu: Modélisation bidimensionnelle de processus non stationnaires et application à l’étude du fond sous-marin. PhD thesis, ENS de Cachan (1998).
V. Pipiras and M.S Taqqu: Are classes of deterministic integrands for fractional Brownian motion on an interval complete? Bernoulli 7 (2001), no 6, pp. 873–897. MR1873833
D. Revuz and M. Yor: Continuous martingales and Brownian motion Volume 293. Springer Science & Business Media, 2013. MR3184878
H. Rootzén: Limit distributions for the error in approximations of stochastic integrals. Ann. Probab. 8 (1980), no. 2, pp. 241–251. MR0566591
F. Russo and P. Vallois: Forward, backward and symmetric stochastic integration Probability theory and related fields 97 (1993), no 3, pp. 403–421. MR1245252
C.A. Tudor: Analysis of the Rosenblatt process ESAIM: Probability and Statistics 12 (2008), pp. 230–257. MR2374640
D. Veneziano, R.L. Bras and J.D. Niemann: Nonlinearity and self-similarity of rainfall in time and a stochastic model. J. Geophysic. Research: Atmospheres 101 (1996), pp. 26371–26392.
T. Vojta, S. Halladay, S. Skinner, S. Janusonis, T. Guggenberger and R. Metzler. Reflected fractional Brownian motion in one and higher dimensions. Phys. Rev. E. 102 (2020), 032108. MR4162529
L.C. Young: An inequality of the Hölder type, connected with Stieltjes integration Acta Mathematica 67 (1936), no 1, pp. 251–282. MR1555421
M. Talagrand: Sur l’intégrabilité des vecteurs gaussiens. Z. Wahrscheinlichkeitstheorie verw. Gebiete 68 (1984), pp. 1–8. MR0767440
M. Zähle: Integration with respect to fractal functions and stochastic calculus. I Probability theory and related fields (1998), no 3, pp.333–374. MR1640795
